Laudrup has enjoyed a fine season in charge of the Swans and guided the club to their first major trophy as they won the Capital One Cup in February.
The Dane has been linked with a host of big jobs across Europe in recent months and while Britton understands why he hopes Laudrup does not leave like Brendan Rodgers did last summer.
"Michael has been fantastic," Britton told the Sunday Express.
"He trusts the players to do their jobs and his signings have been brilliant - especially Michu, Chico and Jonathan de Guzman - and we've had a brilliant season. I just hope we can keep him.
"All the managers have done a good job at the club and moved on. It's no surprise to see Michael linked with a number of jobs, not just here but even in European football.
"But hopefully we can keep him. Continuity is very good and I'm sure he wants to build on our success in the Europa League next season.
"Kenny Jackett was the last one to leave, courtesy of the board's decision, in 2007. The others have been poached. But that shows we are doing well as a football club.
"The board always chooses the right men to succeed the previous manager, but hopefully they can have a summer off."
It has been a remarkable rise for Swansea since Britton first turned out for the club in 2002 and he is still shocked that the Welsh club are seen as the template for success.
"It's amazing for people to use ourselves as a blueprint," he added.
"I'm sure people weren't saying Swansea were a blueprint for everyone when we were at the Vetch Field playing in front of 2,300 people.
"But you have to give great credit to the board. We're a well-run club, making profits, signing good players and improving year on year. It's understandable other clubs will want to be like us.
"There are other clubs who also do things in the right way, the German clubs like Bayern Munich and Borussia Dortmund have also been praised - so maybe we'll be in the Champions League Final one day!
"The team and the club keep improving - so let's hope the club can continue in the right direction."